An approximate solution for the power utility optimization under predictable returns

Abstract

This work presents an approximate solution of the portfolio choice problem for the investor with a power utility function and the predictable returns. Assuming that asset returns follow the vector autoregressive process with the normally distributed error terms (what is a popular choice in financial literature to model the return path) it comes up with the fact that portfolio gross returns appear to be normally distributed as a linear combination of normal variables. As it was shown, the log-normal distribution seems to be a good proxy of the normal distribution in case if the standard deviation of the last one is way much smaller than the mean. Thus, this fact is exploited to derive the optimal weights. Besides, the paper provides a simulation study comparing the derived result to the well-know numerical solution obtained by using a Taylor series expansion of the value function.

Multi-period power utility optimization under stock return predictability

“…by the 4th order Taylor series expansion of the value function (see, Ivasiuk 2019). The comparison is done by simulating the return path and calculating the weights corresponding to the numerical and closed-form solutions, which then are used in the computation of the final utility.…”